Average Error: 0.1 → 0.1
Time: 7.2s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)
double f(double x, double y, double z, double t) {
        double r141371 = x;
        double r141372 = y;
        double r141373 = log(r141372);
        double r141374 = r141371 * r141373;
        double r141375 = r141374 - r141372;
        double r141376 = z;
        double r141377 = r141375 - r141376;
        double r141378 = t;
        double r141379 = log(r141378);
        double r141380 = r141377 + r141379;
        return r141380;
}
↓
double f(double x, double y, double z, double t) {
        double r141381 = y;
        double r141382 = cbrt(r141381);
        double r141383 = r141382 * r141382;
        double r141384 = log(r141383);
        double r141385 = x;
        double r141386 = r141384 * r141385;
        double r141387 = 0.3333333333333333;
        double r141388 = pow(r141381, r141387);
        double r141389 = log(r141388);
        double r141390 = r141389 * r141385;
        double r141391 = r141390 - r141381;
        double r141392 = z;
        double r141393 = r141391 - r141392;
        double r141394 = t;
        double r141395 = log(r141394);
        double r141396 = r141393 + r141395;
        double r141397 = r141386 + r141396;
        return r141397;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - z\right) + \log t\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)} - y\right) - z\right) + \log t\]

  6. Applied associate--l+0.1

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right)} - z\right) + \log t\]

  7. Applied associate--l+0.1

    \[\leadsto \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right)\right)} + \log t\]

  8. Applied associate-+l+0.1

    \[\leadsto \color{blue}{\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)}\]
  9. Using strategy rm

  10. Applied pow1/30.1

    \[\leadsto \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\left(\log \color{blue}{\left({y}^{\frac{1}{3}}\right)} \cdot x - y\right) - z\right) + \log t\right)\]

  11. Final simplification0.1

    \[\leadsto \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)\]

Reproduce

herbie shell --seed 2020039 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))